552 lines
16 KiB
Fortran
552 lines
16 KiB
Fortran
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!
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!=======================================================================
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!
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MODULE SCREENING_VEC2
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!
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USE ACCURACY_REAL
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!
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CONTAINS
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!
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!=======================================================================
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!
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SUBROUTINE SCREENING_VECTOR2(SC_TYPE,DMN,X,RS,T,KS_SI)
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!
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! This subroutine computes the screening vector
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!
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!
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! Input parameters:
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!
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! * SC_TYPE : type of screeening
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! SC_TYPE = 'NO' no screening
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! SC_TYPE = 'IS' Tago-Utsumi-Ichimaru
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! SC_TYPE = 'KL' Kleinman
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! SC_TYPE = 'OC' one-component plasma
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! SC_TYPE = 'RP' RPA
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! SC_TYPE = 'ST' Streitenberger
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! SC_TYPE = 'UI' Utsumi-Ichimaru
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! SC_TYPE = 'YT' Yasuhara-Takada
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! * DMN : dimension of the system
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! * X : dimensionless factor --> X = q / (2 * k_F)
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : system temperature in SI
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!
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!
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! Output parameters:
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!
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! * KS_SI : screening vector expressed in SI
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 9 Oct 2020
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!
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!
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USE REAL_NUMBERS, ONLY : ZERO
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!
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IMPLICIT NONE
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!
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CHARACTER (LEN = 2) :: SC_TYPE,DMN
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!
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INTEGER :: I_KL
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!
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REAL (WP), INTENT(IN) :: X,RS,T
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REAL (WP) :: KS_SI
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!
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I_KL = 1 ! Kleinman switch
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!
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IF(SC_TYPE == 'NO') THEN !
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KS_SI = ZERO !
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ELSE IF(SC_TYPE == 'IS') THEN !
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CALL TUI_VECTOR(DMN,T,RS,KS_SI) !
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ELSE IF(SC_TYPE == 'KL') THEN !
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CALL KLEINMAN_VECTOR(DMN,X,I_KL,KS_SI) !
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ELSE IF(SC_TYPE == 'OC') THEN !
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CALL OCP_VECTOR(DMN,T,KS_SI) !
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ELSE IF(SC_TYPE == 'RP') THEN !
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CALL RPA_VECTOR(DMN,X,KS_SI) !
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ELSE IF(SC_TYPE == 'ST') THEN !
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CALL STREITENBERGER_VECTOR(DMN,RS,KS_SI) !
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ELSE IF(SC_TYPE == 'UI') THEN !
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CALL UTSUMI_ICHIMARU_VECTOR(DMN,RS,KS_SI) !
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ELSE IF(SC_TYPE == 'YT') THEN !
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CALL YASUHARA_TAKADA_VECTOR(DMN,RS,T,KS_SI) !
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END IF !
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!
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END SUBROUTINE SCREENING_VECTOR2
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!
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!=======================================================================
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!
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SUBROUTINE UTSUMI_ICHIMARU_VECTOR(DMN,RS,K_WS_SI)
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!
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! This subroutine computes the Utsumi-Ichimaru screening vector
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! used for computing the screening static structure factor
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!
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! Reference: K. Utsumi and S. Ichimaru, Phys. Rev. B 22,
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! 5203-5212 (1980)
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!
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!
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! Input parameters:
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!
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! * DMN : dimension of the system
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! * RS : Wigner-Seitz radius (in units of a_0)
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!
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!
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! Output parameters:
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!
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! * K_WS_SI : screening vector expressed in SI
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 5 Oct 2020
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!
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!
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USE REAL_NUMBERS, ONLY : ZERO,TWO,THREE,HALF
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USE PI_ETC, ONLY : PI_INV
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USE FERMI_SI, ONLY : KF_SI
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USE UTILITIES_1, ONLY : ALFA
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USE ENERGIES, ONLY : EC_TYPE
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USE CORRELATION_ENERGIES
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!
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IMPLICIT NONE
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!
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CHARACTER (LEN = 2) :: DMN
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!
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REAL (WP), INTENT(IN) :: RS
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REAL (WP), INTENT(OUT) :: K_WS_SI
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!
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REAL (WP) :: ALPHA,EC,D_EC_1,D_EC_2
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!
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IF(DMN /= '3D') THEN !
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K_WS_SI = ZERO !
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GO TO 10 !
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END IF !
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!
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ALPHA = ALFA('3D') !
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!
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! Computing the correlation energy and its derivatives
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!
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EC = EC_3D(EC_TYPE,1,RS,ZERO) !
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CALL DERIVE_EC_3D(EC_TYPE,1,5,RS,ZERO,D_EC_1,D_EC_2) !
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!
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K_WS_SI = KF_SI * ( THREE * HALF * PI_INV - ALPHA * ( & !
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RS * RS * EC + TWO * RS * D_EC_1 ) & ! ref. (1) eq. (38)
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) !
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!
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10 RETURN
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!
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END SUBROUTINE UTSUMI_ICHIMARU_VECTOR
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!
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!=======================================================================
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!
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SUBROUTINE KLEINMAN_VECTOR(DMN,X,I_KL,K_KL_SI)
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!
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! This subroutine computes the Kleinman screening vector
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!
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! Reference: (1) : P. R. Antoniewicz and L. Kleinman, Phys. Rev. B 2,
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! 2808-2811 (1970)
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!
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!
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! Input parameters:
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!
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! * DMN : dimension of the system
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! * X : dimensionless factor --> X = q / (2 * k_F)
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! * I_KL : switch
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! I_KL = 1 : for coefficient A
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! I_KL = 2 : for coefficient B
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!
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!
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!
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! Output parameters:
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!
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! * K_KL_SI : screening vector expressed in SI
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 5 Oct 2020
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!
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!
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!
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USE REAL_NUMBERS, ONLY : ZERO,ONE,TWO,HALF
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USE FERMI_SI, ONLY : KF_SI
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USE LINDHARD_FUNCTION, ONLY : LINDHARD_S
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USE SCREENING_VEC, ONLY : THOMAS_FERMI_VECTOR
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!
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IMPLICIT NONE
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!
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CHARACTER (LEN = 2) :: DMN
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!
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INTEGER, INTENT(IN) :: I_KL
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP), INTENT(OUT) :: K_KL_SI
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!
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REAL (WP) :: ALF,K2
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REAL (WP) :: Q_SI,K_TF_SI,LR,LI,Z2
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!
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REAL (WP) :: EXP,SQRT
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!
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IF(DMN /= '3D') THEN !
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K_KL_SI = ZERO !
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GO TO 10 !
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END IF !
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!
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Q_SI = TWO * X * KF_SI ! q in SI
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!
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ALF = HALF * (ONE + EXP(-X)) ! ref. (1) eq. (21)
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!
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IF(I_KL == 1) THEN !
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K2 = TWO * ALF * KF_SI * KF_SI !
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ELSE IF(I_KL == 2) THEN !
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K2 = TWO * KF_SI * KF_SI * (ALF + TWO * X * X) !
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END IF !
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!
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! Computing the Thomas-Fermi screening vector
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!
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CALL THOMAS_FERMI_VECTOR(DMN,K_TF_SI) !
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!
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Z2 = K_TF_SI * K_TF_SI / (Q_SI * Q_SI) ! (q_{TF}/q)^2
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!
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! Computing the RPA static dielectric function:
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!
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! epsilon(q) = 1 + (q_{TF}/q)^2 * LR
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!
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CALL LINDHARD_S(X,DMN,LR,LI) !
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!
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K_KL_SI = SQRT(K2 * Z2 * LR) ! ref. (1) eq. (20)
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!
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10 RETURN
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!
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END SUBROUTINE KLEINMAN_VECTOR
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!
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!=======================================================================
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!
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SUBROUTINE STREITENBERGER_VECTOR(DMN,RS,K_ST_SI)
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!
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! This subroutine computes the Streintenberger screening vector
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!
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! Reference: (1) : P. Streintenberger, Phys. Stat. Sol. (b) 125,
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! 681-692 (1984)
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!
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!
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! Input parameters:
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!
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! * DMN : dimension of the system
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! * RS : Wigner-Seitz radius (in units of a_0)
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!
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!
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!
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! Output parameters:
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!
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! * K_ST_SI : screening vector expressed in SI
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 6 Oct 2020
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!
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!
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!
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USE DIMENSION_CODE, ONLY : NSIZE
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USE REAL_NUMBERS, ONLY : ZERO,ONE,FOUR,HALF
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USE PI_ETC, ONLY : PI
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USE FERMI_SI, ONLY : KF_SI
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USE FIND_ZERO, ONLY : FIND_ZERO_FUNC
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!
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IMPLICIT NONE
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!
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CHARACTER (LEN = 2) :: DMN
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!
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INTEGER :: I
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!
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INTEGER, PARAMETER :: N_MAX = 400 ! max. number of points
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!
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REAL (WP), INTENT(IN) :: RS
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REAL (WP), INTENT(OUT) :: K_ST_SI
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!
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REAL (WP) :: CC,YY,ZEROF
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REAL (WP) :: Y(NSIZE),F(NSIZE)
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!
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REAL (WP), PARAMETER :: Y_MAX = 16.0E0_WP ! max. value of (K_ST_SI / KF_SI)^2
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!
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REAL (WP) :: FLOAT,LOG,SQRT
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!
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IF(DMN /= '3D') THEN !
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K_ST_SI = ZERO !
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GO TO 10 !
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END IF !
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!
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CC = PI * KF_SI !
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!
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! Constructing the function whose zero is seeked
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!
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! Abscissa : Y = (K_ST_SI / KF_SI)^2
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!
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DO I = 1, N_MAX !
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Y(I) = FLOAT(I) * Y_MAX / FLOAT(N_MAX) !
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YY = Y(I)
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F(I) = YY * (CC - HALF + YY * LOG(ONE + FOUR / YY)) - FOUR ! ref. (1) eq. (59)
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END DO !
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!
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! Finding the zero
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!
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CALL FIND_ZERO_FUNC(Y,F,N_MAX,ZEROF) !
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!
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K_ST_SI = KF_SI * SQRT(ZEROF) !
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!
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10 RETURN
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!
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END SUBROUTINE STREITENBERGER_VECTOR
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!
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!=======================================================================
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!
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SUBROUTINE YASUHARA_TAKADA_VECTOR(DMN,RS,T,K_YT_SI)
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!
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! This subroutine computes the Yasuhara-Takada screening vector
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!
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! Reference: (1) : H. Yasuhara and Y. Takada, Phys. Rev. B 43,
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! 7200-7211 (1991)
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!
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!
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! Input parameters:
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!
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! * DMN : dimension of the system
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : system temperature in SI
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!
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!
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!
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! Output parameters:
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!
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! * K_YT_SI : screening vector expressed in SI
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!
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!
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! Note: We use here the fact that the isothermal compressibility
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! can be expressed as :
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!
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! K_T^0 4
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! 1 - ------- = ---- alpha RS * gamma_0(RS)
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! K_T pi
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!
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! Author : D. Sébilleau
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!
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! Last modified : 6 Oct 2020
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!
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!
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USE REAL_NUMBERS, ONLY : ZERO,ONE,TWO,FOUR
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USE PI_ETC, ONLY : PI_INV
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USE GAMMA_ASYMPT, ONLY : GAMMA_0_3D
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USE UTILITIES_1, ONLY : ALFA
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USE SCREENING_VEC, ONLY : THOMAS_FERMI_VECTOR
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!
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IMPLICIT NONE
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!
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CHARACTER (LEN = 2) :: DMN
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!
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REAL (WP), INTENT(IN) :: RS,T
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REAL (WP), INTENT(OUT) :: K_YT_SI
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!
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REAL (WP) :: G0,ALPHA
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REAL (WP) :: K0K,K_TF_SI
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!
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REAL (WP) :: SQRT
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!
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IF(DMN /= '3D') THEN !
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K_YT_SI = ZERO !
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GO TO 10 !
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END IF !
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!
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G0 = GAMMA_0_3D(RS,T) ! gamma_0(RS)
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!
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ALPHA = ALFA('3D') !
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!
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K0K = ONE - FOUR * PI_INV * ALPHA * RS * G0 ! K_T^0 / K_T
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!
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CALL THOMAS_FERMI_VECTOR('3D',K_TF_SI) !
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!
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K_YT_SI = K_TF_SI / SQRT(TWO - K0K) ! ref. (1) eq. (3.31)
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!
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10 RETURN
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!
|
||
|
|
END SUBROUTINE YASUHARA_TAKADA_VECTOR
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE OCP_VECTOR(DMN,T,K_OC_SI)
|
||
|
|
!
|
||
|
|
! This subroutine computes the one-component plasma screening vector
|
||
|
|
!
|
||
|
|
! Reference: (1) : S. V. Adamjan, I. M. Tkachenko,
|
||
|
|
! J.L. Munoz-Cobo Gonzalez and G. Verdu Martin,
|
||
|
|
! Phys. Rev. E 48, 2067-2072 (1993)
|
||
|
|
! (2) : N. G. Nilsson, Phys. Stat. Sol. (a) 19, K75 (1973)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Input parameters:
|
||
|
|
!
|
||
|
|
! * DMN : dimension of the system
|
||
|
|
! * T : system temperature in SI
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * K_YT_SI : screening vector expressed in SI
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 9 Oct 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE REAL_NUMBERS, ONLY : ONE,TWO,THREE,HALF,THIRD,FOURTH
|
||
|
|
USE PI_ETC, ONLY : SQR_PI
|
||
|
|
!
|
||
|
|
USE PLASMON_SCALE_P, ONLY : NONID
|
||
|
|
USE SPECIFIC_INT_7
|
||
|
|
USE SCREENING_VEC, ONLY : THOMAS_FERMI_VECTOR
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
CHARACTER (LEN = 2) :: DMN
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: T
|
||
|
|
REAL (WP), INTENT(OUT):: K_OC_SI
|
||
|
|
!
|
||
|
|
REAL (WP) :: K_TF_SI
|
||
|
|
REAL (WP) :: TH,U,V,ETA
|
||
|
|
REAL (WP) :: G3O2,FM1O2
|
||
|
|
!
|
||
|
|
REAL (WP) :: LOG,SQRT
|
||
|
|
!
|
||
|
|
TH = ONE / NONID !
|
||
|
|
!
|
||
|
|
! Computing the Thomas-Fermi screening vector
|
||
|
|
!
|
||
|
|
CALL THOMAS_FERMI_VECTOR(DMN,K_TF_SI) !
|
||
|
|
!
|
||
|
|
! Calculation of eta = mu / k_B T from the
|
||
|
|
! relation:
|
||
|
|
! 3 1
|
||
|
|
! F (eta) = --- -----------
|
||
|
|
! 1/2 2 TH^{3/2}
|
||
|
|
!
|
||
|
|
! with
|
||
|
|
!
|
||
|
|
! F (eta) approximated from ref. (2)
|
||
|
|
! 1/2
|
||
|
|
!
|
||
|
|
G3O2 = HALF * SQR_PI ! Gamma(3/2)
|
||
|
|
U = G3O2 * THREE * HALF / (TH*1.5E0_WP) ! ref. (1) eq. (3.5)
|
||
|
|
!
|
||
|
|
V = (THREE * SQR_PI * U * FOURTH)**(TWO * THIRD) ! ref. (2) eq. (8)
|
||
|
|
ETA = LOG(U) / (ONE - U*U) + V - & !
|
||
|
|
V / (0.24E0_WP + 1.08E0_WP * V)**2 !
|
||
|
|
!
|
||
|
|
! Computing the Fermi-Dirac integral F (eta)
|
||
|
|
! -1/2
|
||
|
|
!
|
||
|
|
FM1O2 = FD(ETA,-HALF) !
|
||
|
|
!
|
||
|
|
K_OC_SI = K_TF_SI * SQRT(HALF * SQRT(TH) * FM1O2) ! ref. (1) eq. (3.3)
|
||
|
|
!
|
||
|
|
END SUBROUTINE OCP_VECTOR
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE RPA_VECTOR(DMN,X,K_RP_SI)
|
||
|
|
!
|
||
|
|
! This subroutine computes the RPA screening vector
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Input parameters:
|
||
|
|
!
|
||
|
|
! * DMN : dimension of the system
|
||
|
|
! * X : dimensionless factor --> X = q / (2 * k_F)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * K_RP_SI : screening vector expressed in SI
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 9 Oct 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE LINDHARD_FUNCTION, ONLY : LINDHARD_S
|
||
|
|
USE SCREENING_VEC, ONLY : THOMAS_FERMI_VECTOR
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
CHARACTER (LEN = 2) :: DMN
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: X
|
||
|
|
REAL (WP), INTENT(OUT):: K_RP_SI
|
||
|
|
!
|
||
|
|
REAL (WP) :: K_TF_SI
|
||
|
|
REAL (WP) :: LR,LI
|
||
|
|
!
|
||
|
|
! Computing the Thomas-Fermi screening vector
|
||
|
|
!
|
||
|
|
CALL THOMAS_FERMI_VECTOR(DMN,K_TF_SI) !
|
||
|
|
!
|
||
|
|
! Computing the Lindhard static function
|
||
|
|
!
|
||
|
|
CALL LINDHARD_S(X,DMN,LR,LI) !
|
||
|
|
!
|
||
|
|
K_RP_SI = K_TF_SI * LR !
|
||
|
|
!
|
||
|
|
END SUBROUTINE RPA_VECTOR
|
||
|
|
!
|
||
|
|
!=======================================================================
|
||
|
|
!
|
||
|
|
SUBROUTINE TUI_VECTOR(DMN,RS,T,K_IS_SI)
|
||
|
|
!
|
||
|
|
! This subroutine computes the Tago-Utsumi-Ichimaru screening vector
|
||
|
|
!
|
||
|
|
! Reference: (1) : K. Tago, K. Utsumi and S. Ichimaru,
|
||
|
|
! Prog. Theor. Phys. 65, 54-65 (1981)
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Input parameters:
|
||
|
|
!
|
||
|
|
! * DMN : dimension of the system
|
||
|
|
! * RS : Wigner-Seitz radius (in units of a_0)
|
||
|
|
! * T : system temperature in SI
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Output parameters:
|
||
|
|
!
|
||
|
|
! * K_IS_SI : screening vector expressed in SI
|
||
|
|
!
|
||
|
|
!
|
||
|
|
!
|
||
|
|
! Author : D. Sébilleau
|
||
|
|
!
|
||
|
|
! Last modified : 11 Dec 2020
|
||
|
|
!
|
||
|
|
!
|
||
|
|
USE REAL_NUMBERS, ONLY : TWO
|
||
|
|
USE CONSTANTS_P1, ONLY : BOHR,K_B
|
||
|
|
USE PLASMON_SCALE_P, ONLY : NONID
|
||
|
|
USE THERMODYNAMIC_PROPERTIES, ONLY : U_IT_3D
|
||
|
|
!
|
||
|
|
IMPLICIT NONE
|
||
|
|
!
|
||
|
|
CHARACTER (LEN = 2) :: DMN
|
||
|
|
!
|
||
|
|
REAL (WP), INTENT(IN) :: RS,T
|
||
|
|
REAL (WP), INTENT(OUT):: K_IS_SI
|
||
|
|
!
|
||
|
|
K_IS_SI = - TWO * U_IT_3D(T) / (RS * BOHR * NONID) ! ref. (1) eq. (31)
|
||
|
|
!
|
||
|
|
END SUBROUTINE TUI_VECTOR
|
||
|
|
!
|
||
|
|
END MODULE SCREENING_VEC2
|
||
|
|
|